Nelson Semedo's first goal in Spain's top flight gave Barca a swift start as they sought to restore a five-point lead over Atletico Madrid at the summit, but Ernesto Valverde's men were far from their fluent best and had to wait for Lionel Messi to seal a 2-0 win in the 68th-minute.
Bernardo Espinosa's red card early in the second half had not been enough to derail Girona's challenge, with Marc-Andre ter Stegen making a trio of saves to frustrate Cristhian Stuani.
"In my opinion they play some of the best football in LaLiga. It's always tough to play here," said Alba, who resumed his familiar role of provider to Messi in the game's key moment.
"You have to work really hard to get anything out of the game. They were very well organised with 10 and we couldn't find the space.
"It was a tough game for us but it was a very important win. It was an even game, we won because of the important details.
"We've got quality, especially up front where Leo never fails us. We're happy for Nelson's goal too."
Alba felt the tough challenge presented by Girona is indicative of raised standards across LaLiga from the division's perceived lesser lights.
"They knocked Atlei out of the Copa. They are one of the toughest teams in LaLiga.
"LaLiga is more and more equal every day. The teams who are up there – Madrid, Atletico, us - we have to be there, but it is tough going to every ground. Every match can surprise you and cost you the title."
Barcelona are back in action at Camp Nou on Wednesday in the Copa del Rey, where they will look to recover from a 2-0 first-leg defeat to Sevilla.